Optical rotation of microscopic particles

ABSTRACT

Apparatus for and a method of rotating microscopic objects uses a beam of electromagnetic radiation. A microscopic, non-circularly symmetric distribution of electro-magnetic radiation is projected on to a region containing an object to be rotated so as to cause photons in the beam to refract around the objects. Rotating means then rotate that distribution and so rotate the objects. The distribution may be formed on the interference pattern between a beam having a Laguerre-Gaussian wave fronts and either a plane wave or a further Laguerre-Gaussian beam of opposite helicity.

FIELD OF THE INVENTION

[0001] This invention relates to apparatus for rotating microscopicobjects, and particularly to apparatus which uses a beam ofelectromagnetic radiation to that end. The invention also relates to amethod of rotating a microscopic object using electromagnetic radiation.

BACKGROUND TO THE INVENTION

[0002] The use of optical forces to trap and manipulate micron sizeparticles was pioneered by A Ashkin over ten years ago. [See A. Ashkin,J. M. Dziedzic, J. E. Bjorkholm and S. Chu, Opt. Lett., 11,288 (1986)].He showed that a single, tightly focused laser beam could be used tohold a microscopic particle in three dimensions near the focus of thebeam. Apparatus using a beam in this way provides a powerfulnon-invasive technique for manipulating microscopic particles, and isgenerally known as “optical tweezers”.

[0003] Optical tweezers have firmly established themselves as powerfultools, especially in the field of biology where they have enabled arange of studies to be conducted. This includes work on DNA, colloids,red blood cells, chromosomes and other biological specimens.

[0004] Optical tweezers make use of the optical gradient force: forparticles of higher refractive index than their surrounding medium,photons from the beam are refracted around the particles and thus impartreaction forces (resulting from their change in momentum) on theparticles. The more photons that are refracted in one general direction,the greater the reaction force on the particle in the oppositedirection. This results in various particles migrating towards and beingheld within the region of the beam with the highest light intensity.

[0005] However, conventional optical tweezers provide little or noeffective control over the orientation of the microscopic particleswhich they manipulate.

[0006] The ability to induce controlled rotation of trapped particleswithin optical tweezers potentially offers a new degree of control formicroscopic objects and has significant applications in optical micromachines and biotechnology. To date, two major schemes have successfullyenabled trapped micro objects to be set into rotation. The first schemeemploys Laguerre-Gaussian light beams [H. He, M. E. J. Friese, N. R.Heckenberg, H Rubinsztein-Dunlop, Phys. Rev. Lett., 75 826, (1995); M.E. J. Friese, Enger J, H. Rubinsztein-Dunlop, N. R. Heckenberg, Phys.Rev. A54, 1593-1596 (1996); N. B. Simpson, K. Dholakia, L. Allen and M.J. Padgett, Opt. Lett., 22, 52 (1997)]. Such beams possess an on-axisphase singularity characterised by helical wavefronts. Thus, thePoynting vector in such beams follows a corkscrew-like path as the beamspropagate, and this gives rise as to what is termed as orbital angularmomentum in the light beam [L. Allen, M. W. Beijersbergen, R. J. C.Spreeuw, J. P. Woerdman, Phys. Rev. A45, 8185 (1992)].

[0007] This angular momentum is distinct from any angular momentum dueto the polarisation state of the light and has magnitude of lh where lis one of two indices that describes the mode. Specifically l refers tonumber of complete cycles of phase (2πl) upon going around the modecircumference. However, to transfer orbital angular momentum to atrapped particle with such a beam, the particle must typically absorbsome of the laser light yet still be transparent enough to be tweezed.This in turn restricts the range of particles this method can be appliedto and also further limits this technique in that heating from thisabsorption could damage the rotating particle. Furthermore, as theparticle absorption can be difficult to quantify, controlled rotation oftrapped objects in such a beam is very difficult to realise.

[0008] The other technique for rotation makes use of the change inpolarisation state of light upon passage through a birefringent particle[M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H.Rubinsztein-Dunlop, Nature, 394,348 (1998)]. For example, circularlypolarised light is well known to possess spin angular momentum and thisangular momentum can be exchanged with a birefringent medium (e.g.calcite) upon passage of the beam through the medium.

[0009] This method has achieved rotation rates of a few hundred hertzfor irregular samples of crushed calcite, but it limited solely tobirefringent media, is difficult to control and is thus not widelyapplicable. Thus both these methods have serious shortcoming forrotating optical microcomponents.

SUMMARY OF THE INVENTION

[0010] According to a first aspect of the invention, there is providedapparatus for rotating microscopic objects, the apparatus comprisingbeam projection means for projecting a microscopic, non-circularlysymmetric distribution of electromagnetic radiation onto a regioncontaining such an object so as to cause photons in the beam to refractaround the object, rotating means for rotating the distribution relativeto an object in such a region, wherein, in use, said rotation causesoptical gradient forces to be exerted on the object, in such a way as torotate the object.

[0011] For the purposes of this specification, a distribution of lightis non-circularly symmetric if its outline is non-circularly symmetricand/or if the intensity distribution of light in the distribution isnon-circularly symmetric. A distribution of electromagnetic-radiationmay comprise a non circularly symmetric patch or a plurality of patcheseach of which is, individually, circularly symmetric but which define anon-circularly symmetric distribution.

[0012] Thus, the apparatus uses the optical gradient force to impartcontrolled rotation to microscopic objects. This force is not dependenton a microscopic object being able to absorb the incidentelectromagnetic radiation, nor on any optically anisotropic qualities ofthe object. Thus, the apparatus can be used to impart a controlledrotation (corresponding to the degree of rotation of the distribution)on an object which does not absorb the incident electromagnetic, andwhich is not birefringent.

[0013] In a preferred embodiment the rotation means and beam projectionmeans are incorporated into an interferometer, preferably having beamsplitting means which are adapted to cause an input beam of laserelectromagnetic radiation to be split into two components travellingalong different paths, one of the components may be substantially aplanar wave, the other having helical wave fronts, the interferometerfurther comprising combining means for re-combining the two componentsto create an interference pattern which constitutes that distribution ofelectromagnetic radiation, the rotation means comprising path varyingmeans for varying the effective path length of one of the componentsfrom the splitting means to the combining means.

[0014] Since the distribution is constituted by the interference patternbetween a beam of light having helical wave fronts and one having planewave fronts, the alteration of the relative phase between the twocomponents (with adjustment means) will cause the interference patternto rotate about the axis of the re-combined beam.

[0015] More preferably, the beam splitting means is adapted so that bothcomponents have helical wave fronts, the components having oppositehelicity, the interferometer further comprising combining means forrecombining the two components to create an interference pattern whichconstitutes that distribution of electromagnetic radiation, the rotationmeans comprising path varying means for varying the effective pathlength of one of the components from the splitting means to thecombining means.

[0016] Thereby the distribution comprises a plurality of spot shapedpatches, these having a better definition in their pattern profilegiving improved trapping of particles. A further advantage is that theresulting pattern of spots does not change appreciably either side ofthe focus position making it possible to trap the particles in 3-D,preferably the helical components are Laguerre-Gaussian. The two beamsmay have different azimuthal indices. An interferometer is particularlyadvantageous as it can produce a pattern of output light that canpropagate over a long distance. In addition, the adjustment means cancause the distribution of light projected by the interferometer to berotated, in effect, at its point of creation, and thus avoids the needto provide any further rotatable optical element downstream of theinterferometer.

[0017] Preferably, the path varying means is operable to vary theeffective path length of said other components (i.e. the componenthaving helical wave fronts).

[0018] Preferably, the path varying means comprises adjustabletransmission means for altering the wave length of said other componentover at least part of its path to the combining means.

[0019] Preferably, the path varying means is operable to change the wavelengths, and hence the effective path lengths of the other componentwithout substantially altering the distance travelled by the latter fromthe beam splitting means to the combining means.

[0020] To that end, the transmission means may comprise a transparentmember and means for moving the member relative to the path of the othercomponent of the beam to alter the distance travelled by the latterthrough the transparent member.

[0021] Assuming the member has a higher refractive index than the restof the medium through which said other components of the beam travels,an increase in the length of the path of the other component through themember will correspondingly increase the phase lag between the first andsecond components at the combining means.

[0022] Preferably, the transparent member comprises a transparent platewhich is rotatable about an axis in or near the path of said othercomponent of the beam.

[0023] Alternatively, the transmission means may comprise an elementhaving a heat sensitive refractive index, and control means forcontrolling the temperature of the element, and hence its refractiveindex.

[0024] Preferably also, the path varying means comprises a frequencyshifting means for altering the frequency of one of said components.Preferably, the frequency shifting means comprises at least one andpreferably two acousto-optic modulators.

[0025] The shift in frequency between the two beam components means thatwhen they are recombined and interfere, the resulting pattern rotateswith the frequency difference determining the rotation rate.Importantly, this avoids the limitation that a glass plate has a maximumangle through which the resulting rotation can be accomplished.

[0026] Preferably, the splitting means is such that the other componentof the beam (i.e. the component with helical wave fronts) is aLaguerre-Gaussian beam.

[0027] Preferably, the splitting means comprises a holographic element.

[0028] Conveniently, the interferometer includes a source of laser lightfor providing said input beam.

[0029] The invention also lies in a method for rotating a microscopicobject about a rotational axis spaced from any axis of a circularsymmetry of the object, the method comprising steps of projecting adistribution of light onto the object, said distribution beingnon-circularly symmetric about said rotational axis, and rotating thedistribution about the rotational axis, thereby to exert on the objectan optical gradient force for rotating the latter. Preferably, thedistribution comprises one or more patches.

[0030] Thus, the method can be used to provide controlled rotation ofcircularly symmetric (e.g. spherical) objects which are displaced fromthe axis of rotation or non-circularly symmetric objects which areintersected by the axis.

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The invention will now be described, by way of example only, withreference to the accompanying drawings in which:

[0032]FIG. 1 is a schematic diagram of optical tweezer apparatus inaccordance with a first embodiment of the invention;

[0033]FIG. 2 is a diagrammatic representation of wave fronts of a planewave of laser light;

[0034]FIG. 3 is a similar diagram to FIG. 2, which shows the helicalwave fronts of a Laguerre-Gaussian laser light beam (l=3);

[0035]FIG. 4 is a copy of three images obtained from the apparatus ofFIG. 1, showing three 5 micron silica spheres which have been trapped inthe light pattern produced by the optical tweezers and rotated;

[0036]FIG. 5 is a schematic diagram of optical tweezer apparatus inaccordance with a further embodiment of the invention;

[0037]FIG. 6 illustrates the combination of two Laguerre-Gaussian beams;

[0038]FIG. 7 illustrates interference patterns produced by the apparatusof FIG. 5;

[0039]FIG. 8 is a schematic diagram of optical tweezer apparatus usingthe angular Doppler shift to alter the frequency of a component beam;

[0040]FIG. 9 is a series of images of 1 micron diameter spheres beingheld in a crystalline structure until the laser is switched off; and

[0041]FIG. 10 illustrates various structures which have been made androtated by this method.

[0042]FIG. 11 illustrates the trapping and rotation of particles in 3D;and

[0043]FIG. 12 shows successive photographs of particles rotated andmoved in 3D.

DETAILED DESCRIPTION

[0044] With reference to FIG. 1, an Nd=glass laser 1 of power 1W at 1064nm faces an interferometer 2, the output of which passes to an opticaltweezer assembly 3. The assembly 3 includes a microscope stage andsample cell holder 4 in which the object to be rotated/manipulated isretained. A camera 6 is used to obtain an image, via a microscopeobjective 8, of the sample cell and hence the object therein.

[0045] The interferometer 2 comprises a beam splitter in the form of ahologram element 10 that splits the beam into two components. One ofthose components is a plane wave component 12 which passes straightthrough the hologram element 10 substantially undeflected, and which isin the form of a solid beam. The second component, referenced 14 isdeflected to one side of the component 12 and onto a mirror 16 which ispositioned clear of the path of the component 12, and which is so angledas to direct the component 14 in a direction perpendicular to that ofthe component 12. The hologram element 10 is so arranged that the secondcomponent 14 takes the form of a hollow beam (i.e. a cylinder of light)which is of a Laguerre-Gaussian form. In this particular case, thehologram element 10 is so arranged that the Laguerre-Gaussian beam is anLG l=3 beam. An LG l=2 beam is also generated this way. The appearanceof the components 12 and 14, when viewed end-on, are illustrated at 18and 20 respectively.

[0046] The component 12 is refracted by an angled mirror 22 along a pathat right angles to the path from the laser 1 and into the combiningmeans comprising a beam splitter 24.

[0047] A further mirror 26 reflects the component 14 along a path atright angles to the paths in the mirror 16 and also into the beamsplitter 24. Path varying means in the form of a rotatable glass plate28 is interposed in the path from the mirror 16 to the mirror 26.

[0048] The plate 28 is rotatable about a vertical axis which intersectsthe path taken by the component 14 between the mirrors 16 and 26, and isconnected to a mechanism (not shown) for pivoting the plate 28 aboutthat axis by controlled amounts. Such movements will vary the length ofthe path of the component 14 which lies within the plate 28. Thus, themaximum length of path through the plate 28 will occur when the latteris parallel with the path of the component 14 (i.e. at right angles tothe path of the component 12 from the laser 1 to the mirror 22). Thelength of path taken by the component 14 through the plate 28 will be ata minimum when the plate is at right angles to the path of the component14 and the mirror 16 to the mirror 26.

[0049] The plate 28 has a different refractive index from the rest ofthe medium through which the components 12 and 14 propagate to thesplitter 24. As a result, the velocity of the component 14 (and henceits wave length) will be altered as the component 14 enters the plate28. Thus, the plate 28 causes the phase of the component 14 to lagbehind that of the component 12 by an amount which is related to theangular position of the glass plate (i.e. to the length of path overwhich the wave length of the component 14 is altered).

[0050] The beam splitter 24 has a semi-reflective surface 30 whichtransmits the component 14 (reflected from the mirror 26) and reflectsthe component 12 (reflected from the mirror 22) along a single path 32to an output mirror 34. The interference pattern produced by thecombined beams is illustrated at 36 and comprises a spiral having threearms 38, 40 and 42. The way in which this interference pattern is formedcan be best understood with reference to FIGS. 2 and 3. FIG. 2 shows twowave fronts of the plane wave component 12. These are illustrated as twocircles 36 and 38 on the end faces of an enclosed volume 40 throughwhich the component 12 travels (from the face with the disc 38 to theface with the disc 36).

[0051] With reference to FIG. 3, a Laguerre-Gaussian beam has two modeindices l and p, the index l denoting the number of complete cycles ofphase upon going round the circumference of the mode. As an illustrativeexample, an l=2 or l=3 LG mode can be thought of as a double or triplestart helix respectively. In the present case, the component 14 is in anl=3 LG mode, and the wave fronts therefore form a triple start helixhaving three helical arms, 44 and 46. These forms are shown in a volume40′ which corresponds to the volume 40. Thus, the component 14 travelsfrom the bottom to the top of the volume 40, but as this happens thePoynting vector for the component 14 follows a helical path.Constructive interference of the two components occurs when the wavefronts are in phase with each other, i.e. on the intersection betweenthe form as shown in FIG. 3 with a circle perpendicular to the axis ofthe helix. This gives the three-armed configuration illustrated at FIG.3.

[0052] Moreover, by simply changing the path length of theinterferometer (using the plate 28) it is possible to cause the spiralpattern to rotate in a controlled fashion about its axis. This isbecause the position of the plane wave front (e.g. 36) relative to thehelical wave fronts (42, 44 and 46) will change. As an analogy, this isakin to considering what occurs along a length of thick cord thatconsists of l intertwined ropes. If the cord were successively cut alongits length, and each time the individual ropes at the end of the cordviewed end-on, any given piece of rope in the cord would appear torotate around the cord axis. Moving along the cord is analogous toaltering the altering the optical path length in the interferometer, andchanging the optical path length in the interferometer is akin to achange in the linear momentum of the light. The helical nature of thewave front of the LG component 14 transforms this into a linear momentumchange about the axis of the interference pattern, that is angularmomentum. It will be appreciated that the interferometer 2 could bereadily modified by interposing the glass plate 28 in the path of thecomponent 12 and the laser 1 to the beam splitter 24 so that rotation ofthe plate 28 alters the effective path length, and hence phase of thecomponent 12. Indeed, the interferometer may be further modified byhaving two glass plates, one in the path of each respective component 12and 14. This provides further control over the extent and sense ofrotational movement of the spiral pattern 36. Light from the output ofthe interferometer 2 is passed to the optical tweezer assembly 3 inwhich a steering mirror 48 controls the direction of the output beamwhich passes through two lenses 50 and 52 onto a dielectric mirror 54and then onto the sample cell via a ×40 microscope objective 56. Themirror 48 can be used to manoeuvre the beam so that it can catch aselected object or set of particles, and these particles can then berotated by manipulating the glass plate 28 to cause the spiralinterference pattern to rotate. Light from the cell is also transmittedthrough the objective 8 and onto a mirror 58 which reflects the lightinto a camera 6, the output of which is fed to a visual display unit(not shown) to enable the operation of the tweezers to be monitored.

[0053] Moreover, by simply changing the path length of theinterferometer using the plate 28 we are able to cause the spiralpattern (and thus the trapped particles) to rotate in a controlledfashion about the axis of the spiral pattern. The rotation of thepattern occurs due to the helical nature of the wave fronts of aLaguerre-Gaussian light beam.

[0054] This technique relies on the optical gradient force to tweeze atrapped particle in the spiral arms and then utilises the variation(i.e. rotation) of this spiral pattern under a variation of optical pathlength to induce rotation. The technique can therefore be applied inprinciple to any object or objects that can be optically tweezed, incontrast to the conventional methods of rotation above. This techniquecan be extended to the use of LG beams of differing azimuthal index thusoffering the prospect of trapping and rotating different shaped objectsand groups of objects. The spiral pattern for tweezing too can readilybe varied by use of different LG beams of different azimuthal index.

[0055]FIG. 5 illustrates an alternative and preferred interferometer102. This comprises hologram element 110, and beam splitter 112, therebyproviding two Laguerre-Gaussian components from light supplied by laser101. The two beams are then reflected by mirrors 122 and 126. Apivotable glass plate 128 is provided as before to alter the effectivepath length of one component. Dove prism 129 inverts one of the beams,and so when recombined by beam splitter 130, an interference pattern isproduced which comprises a plurality of spots. This recombination isshown in FIG. 6 which illustrates beam splitter 130, and the resultinginterference pattern upon combination of two incoming Laguerre-Gaussianbeams with opposite helicities. As before the helicity relates to theazimuthal index 1. When the two such beams have equal magnitude ofazimuthal index, the resulting pattern comprises 2 l spots distributedaround an axis. As before the introduction of a path length change inone of the arms of the interferometer allows the pattern to be revolved,with a path length change of (2/λ) leading to full revolution.

[0056] In an alternative embodiment, the two Laguerre-Gaussian beamshave differing azimuthal indices and again have opposite helicity. Thisyields a pattern with an odd number of spots, for example FIG. 7aillustrates the pattern of spots provided when beams of azimuthal index1 and −1 are combined, FIGS. 7b, 7 d and 7 f illustrate the pattern ofspots provided when beams of other equal and opposite azimuthal indicesare combined and FIGS. 7c and 7 e illustrate the corresponding situationaround the focal region due to the interference of two Laguerre-Gaussianbeams with different azimuthal indices and opposite helicity.

[0057] An important advantage of using two Laguerre-Gaussian beams isthat the resulting spots provide enhanced trapping of particles whencompared to the spiral embodiment produced by FIG. 1. This is becausethe spot pattern is better defined, producing sharper gradients. Aprimary advantage is that as the resulting spots do not changeappreciably either side of the focus position, the particles can betrapped in three dimensions. FIG. 7(g) illustrates the pattern of spotsat z=0 (the focal point) and z=z_(R) (the Rayleigh range for l=1 andl=−1 components, where the spots can be seen to have the same shape andthat the only change is gradual broadening away from the focal point.

[0058] The invention further provides an alternative method forachieving continuous rotation of the trapped particle or particles. Theuse of the glass plate as discussed above suffers from the eventuallimitation that there is a maximum angle through which the particle maybe rotated, determined by the range of movement of the glass plate andits thickness. The rotation is caused by a temporal change in the pathlength between the two beam components, and it is envisaged that thiscould instead be achieved by using a frequency shifting device betweeneach of the two beams giving the interference pattern. Preferably, atleast one acousto-optic modulator disposed in one beam of theinterferometer carries out a frequency shift. Typically, twoacousto-optic modulators of slightly mismatched frequency shifts inopposite senses will be used. This is because shifts of tens or hundredsof Hertz are typically required but acousto-optic modulators arecurrently only available for larger shifts. Therefore, a shift of say100 Hertz is best achieved with a first device shifting the frequency bysay 80,000,000 Hz and a second device shifting it in the opposite senseby 79,999,900 Hz. The frequency difference between the two components ofthe beam gives the resulting rotation rate of the pattern. Therefore,the pattern will rotate continuously without having eventual limits.

[0059] An alternative method of arranging a frequency shift is to usethe socalled angular doppler shift. Here a rotating plate, such as ahalf-wave plate, is placed in one component of the beam, transferringangular momentum to circulary polarised light which passes therethrough,altering its frequency.

[0060]FIG. 8 is an illustrative embodiment, corresponding to that ofFIG. 5 with the addition of a rotating half-wave plate 204 giving thedesired frequency shift by means of the angular doppler effect. In orderfor the angular doppler effect to work, circularly polarised light isproduced by quarter wavelength plate 206. A second quarter wavelengthplate 208 in the other component beam path ensures both components havecorresponding polarities. Half wavelength plate 210 is adjustable toalign the polarisation of the incident laser beam to give two equaloutputs from beam splitter 112, output mirror 212 reflects a secondoutput beam from beam splitter 130 to give a second optical tweezer.

[0061] Illustrative examples of rotations by the apparatus of FIG. 1using LG modes l=2 and l=3, will now be described.

[0062] The beam from the laser 1 was directed through the holographicelement 10 that yielded an LG beam 14 in its first order with anefficiency of 30%. This LG beam is then interfered with the zeroth orderbeam 12 from the hologram to generate the spiral interference pattern.This pattern is directed through either a ×40 microscope objective 56 ina standard optical tweezer geometry (applicants have also used a 100×objective in place of the objective 56). Typically around 1 mW-13 mW oflaser light was incident on the trapped structure in the opticaltweezers, with losses due to optical components and the holographicelement. The second microscope objective 8 and CCD camera 6 were usedfor observation purposes.

[0063] It is important to ensure exact overlap of the components 12 and14 at the beam splitter 24 to ensure spiral arms are observed in theinterference pattern—at larger angles linear fringe patterns (with someasymmetry) can result. To set trapped structures into rotation therelative path length between the two components 12 and 14 is altered.This was achieved by placing a glass plate 28 on a rotation stage in onearm (i.e. the path of component 14). Simply by rotating this, theapplicants were able to rotate the pattern in the tweezers. This controlcan be realised in other ways such as the use of a thermally controlledetalon or electro-optic devices (instead of the plate 28) furthersimplifying the experimental arrangement. It is noted that changing thepath length in one arm by l×λ will cause a full rotation of 360 degreesof the pattern (and thus the trapped particle array) in the opticaltweezers. Thus, in contrast to other rotation methods, the inventionprovides a very simple way of controlling both the sense and rate ofrotation of our optically trapped structure.

[0064] The rotation of trapped particles in an interference patternbetween a LG (l=3) mode and a plane wave can be seen in FIG. 4. Thenumber of spiral arms in the pattern is equivalent to the azimuthalindex of the LG mode used. In FIG. 4 we see three trapped 5 micronsilica spheres in this pattern. One of the spheres (60) has a slightdeformity and the series of pictures charts the progress of thisstructure of spheres as the pattern is rotated. Typically rotation ratesof 5 Hz were achieved. The rotation rates were solely limited by theamount of optical power (−13 mW) in the interference pattern. The use ofoptimised components could lead to rotation rates of tens to hundreds ofhertz. The use of a 100× objective (as objective 56) here meant thatfull three-dimensional trapping of a structure of 1 micron spheres wasalso achieved. FIG. 9 is an image of eight 1 micron diameter spheresbeing held in a 2×2×2 cubic array using a combination of beams with l=+2and l=−2 (FIG. 9(a)) and then drifting apart when the laser is switchedoff.

[0065]FIG. 10 illustrates further structures which have also beentrapped and rotated. FIG. 10 shows that one, two or more layers ofparticles can be readily achieved. Custom configurations can be madeexperimentally by moving the beam or sample to pick up individualparticles in specific spots. Sufficiently rapid translation can be usedto dislodge one or more particles. The BCC structure shown in FIG. 10(a)can be made by adding an additional, standard Gaussian beam to hold thecentral particle.

[0066]FIG. 11 illustrates light intensities used in rotating particleswith (a) l=1, l=−1 and (b) l=2, l=−2. FIG. 12 illustrates two particlesrotated in the configuration of FIG. 11(a) and moved in the z-directionas can be seen by the background moving into focus. This shows that true3D trapping and movement have been achieved.

[0067] One can envisage more complicated microfabricated objects beingrotated in the same fashion. Furthermore, silica spheres coated withstreptavidin can bind to DNA and thus one could potentially rotationallyorient DNA strands or other biological biotinylated specimens with thismethod.

[0068] The member 10 may be interchanged with other holographic membersarranged to produce different LG modes for component 14.

[0069] The use of an LG l=2 mode, for example, results in two spiralarms for the interference pattern 36. This pattern has been used torotate a glass rod in the cell. This version of the apparatus thereforeconstitutes an all-optical micro-stirrer and has potential applicationfor optical micromachines and motors. As a final example a chinesehamster chromosome was rotated in the applicants' tweezer assembly 3using this same interference pattern with the axis of the pattern placedover the centromere of the chromosome. This degree of flexibility couldbe used for suitably orienting the chromosome prior to optically cuttingsections for example from one of the sister chromatids.

[0070] The use of an LG l=2 mode in the LG-LG interferometer createsfour spots. Small, 1 micron sizes spheres can be stacked in each of thespots thus creating 3D structures that are crystalline. This can readilybe extended using other LG modes to more complex three-dimensionalstructures and lattices.

[0071] In conclusion, the applicants have demonstrated a technique tocontrollably rotate optically trapped micro-objects. The technique usedby the apparatus is widely applicable as it solely relies on the abilityto tweeze a micro-object and not on any further intrinsic particleproperty. Experiments have shown the controlled rotation of trappedstructures of silica spheres, glass rods and also a chinese hamsterchromosome. The crystal-like 3D structures discussed have also beentrapped and rotated in the light patterns as discussed above. The degreeof rotation is fully controllable, does not cause any heating to thetrapped sample and should find widespread applications with optical andbiological micromachines.

1. Apparatus for rotating microscopic objects, the apparatus comprisingbeam projection means for projecting a microscopic, non-circularlysymmetric distribution of electro-magnetic radiation onto a regioncontaining such an object so as to cause photons in the beam to refractaround the object, rotating means for rotating the distribution relativeto an object in such a region, wherein, in use, said rotation causesoptical gradient forces to be exerted on the object, in such a way as torotate the object.
 2. Apparatus according to claim 1, in which therotation means and beam projection means are incorporated into aninterferometer.
 3. Apparatus according to claim 2, in which theinterferometer has beam splitting means for causing an input beam oflaser electromagnetic radiation to be split into two componentstravelling along different paths, the interferometer further comprisingcombining means for re-combining the two components to create aninterference pattern which constitutes that distribution ofelectro-magnetic radiation, the rotation means comprising path varyingmeans for varying the effective path length of one of the componentsfrom the splitting means to the combining means.
 4. Apparatus accordingto claim 3, in which the beam splitting means is adapted to cause one ofthe components to be substantially a planar wave and the other componentto have helical wave fronts.
 5. Apparatus according to claim 3, in whichthe beam splitting means is adapted to cause both components to havehelical wave fronts, with the components having opposite helicity. 6.Apparatus according to claim 5, in which the beam splitting means isadapted to cause the two beams to have different azimuthal indices. 7.Apparatus according to any one of claims 4 to 6, in which the or eachcomponent having helical wave fronts is a Laguerre-Gaussian beam. 8.Apparatus according to any one of claims 3 to 7, in which theinterferometer includes adjustment means for altering the relative phasebetween the two components, causing the interference pattern to rotateabout the axis of the recombined beam.
 9. Apparatus according to any oneof claims 4 to 8, in which the path varying means is operable to varythe effective path length of the or each component having helical wavefronts.
 10. Apparatus according to any one of claims 4 to 9 wherein thepath varying means comprises adjustable transmission means for alteringthe wave length of the or each component having helical wave fronts overat least part of its path to the combining means.
 11. Apparatusaccording to claim 10 in which the path varying means is operable tochange the wave lengths, and hence the effective path lengths of thecomponent having helical wave fronts without substantially altering thedistance travelled by the latter from the beam splitting means to thecombining means.
 12. Apparatus according to claim 10 or claim 11, inwhich the transmission means comprises a transparent member and meansfor moving the member relative to the path of the or each component ofthe beam having helical wave fronts to alter the distance travelled bythe latter through the transparent member.
 13. Apparatus according toany one of claims 3 to 10 wherein the path varying means comprises afrequency shifting means for altering the frequency of one of saidcomponents.
 14. Apparatus according to any of the preceding claims inwhich the distribution of electro-magnetic radiation comprises anon-circularly symmetric patch or a plurality of patches each of whichis, individually, circularly symmetric but which defines anon-circularly symmetric distribution.
 15. Apparatus according to any ofclaims 2 to 13, in which the interferometer includes a source of laserlight.
 16. Apparatus according to claim 4, in which the beam splittingmeans comprises a holographic element.
 17. A method for rotating amicroscopic object about a rotational axis spaced from any axis of acircular symmetry of the object, the method comprising steps ofprojecting a patch of light onto the object, said patch beingnon-circularly symmetric about said rotational axis, and rotating thepatch about the rotational axis, thereby to exert on the object anoptical gradient force for rotating the latter.
 18. Apparatussubstantially as described herein with reference to, and as illustratedin FIGS. 1 to 4 of the accompanying drawings.
 19. Apparatussubstantially as described herein with reference to, and as illustratedin, FIGS. 5 to 7 of the accompanying drawings.
 20. A methodsubstantially as described herein with reference to FIGS. 1 to 4 of theaccompanying drawings.
 21. A method substantially as described hereinwith reference to FIGS. 5 to 7 of the accompanying drawings.